cee167-fa00-mt1-Ibbs-soln - CE 167 Midterm #1 Fall 2000...

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CE 167 Midterm #1 Fall 2000 Prof. C.W. Ibbs Question #1 [15 Points] The amount of $600 per year is to be paid into an account over each of the next 4 years. The nominal interest rate is 15% per year. Determine the total amount the account will eventually contain under the following conditions: (a) Deposits are made at the beginning of the year with interest compounding yearly: NFV = [$600 (F/A, 15%, 4)](1+i) NFV = $600 ) 1 ( 1 ) 1 ( i i i n + + NFV = $600 ) 15 . 0 1 ( 15 . 0 1 ) 15 . 0 1 ( 4 + + NFV = $344.45.43 (b) Deposits at the end of the year with interest compounding yearly: NFV = [$600(F/A, 15%, 4)] This is the same as the Part (a), except you do not have to account for the extra year of interest NFV = $600 + 15 . 0 1 ) 15 . 0 1 ( 4 = $2996.03 For Parts (a) & (b), 3 points were awarded for the correct usage of the formula, and 2 points for the correct answer. (c) $50 deposits are made at the end of each month with interest compounding monthly: Since i = 15% is a nominal yearly rate , you must find i effective : i effective = 1 1 + m m r = 1 12 15 . 0 1 12 + = 16.08% i effective = 16.08% per year = 1.34% per month This part was worth 1 point A=$600 F=? Because the equations are set up so that payment are made at the end of the year , you have to account for the one extra year’s worth of interest made by making the deposit at the beginning of the year! A=$600 F=? 0 1 2 3 0 1 2 3
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effective , 48)] (48 payments = 12 months/year times 4 years) NFV = $50 + 0134 . 0 1 ) 0134 . 0 1 ( 48 = $3337.50 The use of the correct equation (after finding i effective ) was worth 3 points; the correct answer was worth 1 point. Question #2 [15 Points] You are considering buying office space. You can buy two small office buildings or one large office building. The small buildings cost $1,000,000 apiece and have a resale value of $1,100,000 apiece after two years. The large office building costs $2,200,000 and has a resale value of $2,350,000 after two years. The purchase of the two small buildings will provide a total of $40,000 of net income per year. The purchase of the large office will provide a total of $50,000 of net income per year. Your MARR is 4%. On the basis of an internal rate of return comparison, which option would you choose? Why? (Net income is accrued at the end of the year.) Option 2 Small Buildings 1 Large Building Initial Cost $2,000,000 $2,200,000 Yearly Benefit $40,000 $50,000 Salvage $2,200,000 $2,350,000 MARR = 4% 2 Small Buildings : NPV = 0 = -$2M + + + + + + 2 2 1 ) 1 ( 2 . 2 $ ) 1 ( 40 $ ) 1 ( 40 $ i M i k i k NPV is approximately 0 when i = 7%, therefore the IRR 2small = 7% > MARR; this is a viable option! Solving for the IRR = 5 points
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cee167-fa00-mt1-Ibbs-soln - CE 167 Midterm #1 Fall 2000...

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